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79 lines
2.1 KiB
Python
79 lines
2.1 KiB
Python
from __future__ import annotations
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import sys
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from dataclasses import dataclass
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INT_MIN = -sys.maxsize + 1
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INT_MAX = sys.maxsize - 1
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@dataclass
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class TreeNode:
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val: int = 0
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left: TreeNode | None = None
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right: TreeNode | None = None
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def max_sum_bst(root: TreeNode | None) -> int:
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"""
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The solution traverses a binary tree to find the maximum sum of
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keys in any subtree that is a Binary Search Tree (BST). It uses
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recursion to validate BST properties and calculates sums, returning
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the highest sum found among all valid BST subtrees.
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>>> t1 = TreeNode(4)
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>>> t1.left = TreeNode(3)
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>>> t1.left.left = TreeNode(1)
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>>> t1.left.right = TreeNode(2)
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>>> print(max_sum_bst(t1))
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2
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>>> t2 = TreeNode(-4)
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>>> t2.left = TreeNode(-2)
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>>> t2.right = TreeNode(-5)
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>>> print(max_sum_bst(t2))
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0
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>>> t3 = TreeNode(1)
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>>> t3.left = TreeNode(4)
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>>> t3.left.left = TreeNode(2)
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>>> t3.left.right = TreeNode(4)
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>>> t3.right = TreeNode(3)
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>>> t3.right.left = TreeNode(2)
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>>> t3.right.right = TreeNode(5)
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>>> t3.right.right.left = TreeNode(4)
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>>> t3.right.right.right = TreeNode(6)
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>>> print(max_sum_bst(t3))
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20
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"""
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ans: int = 0
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def solver(node: TreeNode | None) -> tuple[bool, int, int, int]:
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"""
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Returns the maximum sum by making recursive calls
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>>> t1 = TreeNode(1)
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>>> print(solver(t1))
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1
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"""
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nonlocal ans
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if not node:
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return True, INT_MAX, INT_MIN, 0 # Valid BST, min, max, sum
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is_left_valid, min_left, max_left, sum_left = solver(node.left)
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is_right_valid, min_right, max_right, sum_right = solver(node.right)
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if is_left_valid and is_right_valid and max_left < node.val < min_right:
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total_sum = sum_left + sum_right + node.val
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ans = max(ans, total_sum)
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return True, min(min_left, node.val), max(max_right, node.val), total_sum
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return False, -1, -1, -1 # Not a valid BST
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solver(root)
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return ans
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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